Displaying similar documents to “Diffusion Monte Carlo method: Numerical Analysis in a Simple Case”

Stochastic Lagrangian method for downscaling problems in computational fluid dynamics

Frédéric Bernardin, Mireille Bossy, Claire Chauvin, Jean-François Jabir, Antoine Rousseau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This work aims at introducing modelling, theoretical and numerical studies related to a new downscaling technique applied to computational fluid dynamics. Our method consists in building a local model, forced by large scale information computed thanks to a classical numerical weather predictor. The local model, compatible with the Navier-Stokes equations, is used for the small scale computation (downscaling) of the considered fluid. It is inspired by Pope's works on turbulence, and...

An introduction to probabilistic methods with applications

Pierre Del Moral, Nicolas G. Hadjiconstantinou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This special volume of the ESAIM Journal, , contains a collection of articles on probabilistic interpretations of some classes of nonlinear integro-differential equations. The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, including physics, biology, fluid mechanics, molecular chemistry, financial mathematics and bayesian statistics. In this preface, we provide...

Resolution of the time dependent equations by a Godunov type scheme having the diffusion limit

Patricia Cargo, Gérald Samba (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the model to approximate the time dependent transport equation in one dimension of space. In a diffusive regime, the solution of this system is solution of a diffusion equation. We are looking for a numerical scheme having the diffusion limit property: in a diffusive regime, it has to give the solution of the limiting diffusion equation on a mesh at the diffusion scale. The numerical scheme proposed is an extension of the Godunov type scheme proposed by...

Quantitative concentration inequalities on sample path space for mean field interaction

François Bolley (2010)

ESAIM: Probability and Statistics

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We consider the approximation of a mean field stochastic process by a large interacting particle system. We derive non-asymptotic large deviation bounds measuring the concentration of the empirical measure of the paths of the particles around the law of the process. The method is based on a coupling argument, strong integrability estimates on the paths in Hölder norm, and a general concentration result for the empirical measure of identically distributed independent paths. ...

Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications

Jürgen Geiser (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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Our studies are motivated by a desire to model long-time simulations of possible scenarios for a waste disposal. Numerical methods are developed for solving the arising systems of convection-diffusion-dispersion-reaction equations, and the received results of several discretization methods are presented. We concentrate on linear reaction systems, which can be solved analytically. In the numerical methods, we use large time-steps to achieve long simulation times of about 10 000 years. We...

Euler schemes and half-space approximation for the simulation of diffusion in a domain

Emmanuel Gobet (2001)

ESAIM: Probability and Statistics

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This paper is concerned with the problem of simulation of ( X t ) 0 ≤ t ≤ T , the solution of a stochastic differential equation constrained by some boundary conditions in a smooth domain D : namely, we consider the case where the boundary ∂ D is killing, or where it is instantaneously reflecting in an oblique direction. Given N discretization times equally spaced on the interval [ 0 , T ] , we propose new discretization schemes: they are fully implementable and provide a weak error of order N - 1 under some conditions....